Stephen Hester, chief executive of Royal Bank of Scotland, has bowed to intense political pressure and waived a bonus of nearly £1m.

After a weekend of intense scrutiny of the bonus, culminating in a move by Labour to force a Commons vote on the payment, Hester decided he would not accept the 3.6m shares that the bank's board had decided to award him on Thursday.

Hester, parachuted in to run the bank after it was bailed out by the taxpayer in October 2008, is understood to have felt his pay was too much of a distraction to the running of a bank that is 82% owned by the taxpayer. The taxpayers' stake is now valued at around half the £45bn it was worth when it was bailed out.

Labour leader Ed Miliband said last night: "Stephen Hester has done the right thing. It is a shame out-of-touch David Cameron did not realise he should also do the right thing. "

"Labour was right to seek a parliamentary vote on this so that the people's voice could be heard. But the debate about fair executive pay and responsible capitalism is only just beginning. We need a government that will tax bankers' bonuses and bring responsibility to the boardroom."

Hester made the decision last night while on holiday in Switzerland.

Chancellor George Osborne welcomed the move, although this did not quell the intense criticism of the government's handling of the bonus, which from the moment it was announced sparked a wave of protests focusing on pledges ministers had made beforehand to ensure the bonus for Hester was lower than last year.

Due to the complexity of boardroom pay deals, Hester's decision to waive this award of shares does not stop him receiving other multimillion-pound awards of shares through long-term performance plans. His total package, due to be formally announced in March, may still amount to £8m.

The saga has also raised questions about the way RBS is run – at "arm's length" from the taxpayer through UK Financial Investments. Scotland's first minister, Alex Salmond, said: "This is a welcome development, but it should never have come to this stage as these circumstances cannot be left to individual decisions. They must be a matter of public policy …

"The sustaining of public services, and therefore economic recovery, requires pay restraint across the public sector.

"How can that be maintained against the background of huge bonuses being paid in organisations which are still within the public sector? This blatant inequality thus threatens economic recovery."

The timing of the bonus announcement coincided with a move by the coalition to announce a crackdown on executive pay by giving shareholders more powers to vote on pay deals. The shadow business secretary, Chuka Umunna, told Sky News Hester was "doing the right thing".

"It's a shame that the government, having gone around lecturing shareholders in other large companies to take an active role in bringing about wage restraint, chose to sit on its hands in this case and that it took so long for there to be a public clamour and row of this order for the change in position that we have just witnessed to take place," Umunna said. Lib Democrat peer Lord Oakeshott said Hester had "bowed to the inevitable" but kept up the pressure on the prime minister, who, he said, "had shown very poor judgment".

A political row had erupted immediately after the bonus was awarded over whether the government could have done more to stop any bonus being paid to Hester. After Hester's late-night decision had been announced, Osborne said: "This is a sensible and welcome decision that enables Stephen Hester to focus on the very important job he has got to do, namely to get back billions of pounds of taxpayers' money that was put into RBS."

However, the chancellor had previously been defending the bonus award as the government had been blaming Labour for Hester's contract.

The Treasury minister Danny Alexander had claimed on the BBC's Sunday Politics, before the decision by Hester to waive the share award, that the only way to halt bonuses was to take direct control of the bank, which would heap further losses on the public.

Pressure had also come from the work and pensions secretary, Iain Duncan Smith, who had said the decision not to take any bonus lay with Hester. Asked on the Andrew Marr Show whether Hester should take his bonus, Duncan Smith said: "It's for him individually, obviously, to make a decision about that. As a member of the government, I don't have a collective opinion on that but I must say to you nobody would be happier than the government if of course he took such decisions, but it's up to him."